Energy efficient zone‐based clustering algorithm using fuzzy inference system for wireless sensor networks

In Wireless Sensor Networks (WSN), as sensor nodes have limited energy, the design of an energy‐efficient clustering technique is a critical challenge to be addressed. We propose an Energy‐Efficient Zone‐based Clustering algorithm for WSN that works efficiently in large area WSN as well. In the proposed method, the sensing field is divided into equal size zones, and one Zone Monitor is selected in each zone. The distance of a Zone Monitor from the Base Station is considered in the calculation of the number of desired Cluster Heads (CHs) in its zone for implementing Unequal clustering. The CHs are selected such that they are uniformly distributed inside each zone to conserve the energy of sensor nodes needed for intra‐cluster transmission. Also, for better load balancing among the selected CHs, we propose that cluster size should be uniform at zone level. Hence, after the CHs are selected, the remaining sensor nodes in a zone decide to become a cluster member of one of the selected CHs using a fuzzy‐based cluster formation technique. We compare the proposed algorithm with other approaches for three different network scenarios using parameters such as the number of alive nodes, the first node dies, half of the nodes die, the last node dies, the amount of data received at Base Station, and total remaining energy. Simulation results show that the proposed clustering algorithm provides better performance than other methods.

intervention is not possible. For example, WSN could be used in a dense forest area for early fire detection and also for analyzing the behavior of various species. In such cases, it is difficult to gather complete information in different environmental conditions by humans directly. WSNs can monitor various conditions such as humidity, pressure, vibration, temperature, and stress.
Sensor nodes have limited resources, such as processing capabilities, energy, and storage. Energy is a critical resource in WSN, and it determines the whole network's lifetime. As each sensor node has its battery onboard for power supply, which is non-rechargeable and non-changeable, it is essential to optimize energy consumption to use as little power as possible. Researchers have suggested various schemes for utilizing energy efficiently while doing the basic operations of sensing and data transmission. Among these several schemes, hierarchical approaches like clustering are most promising. In the clustering technique, the sensor nodes in the network are formed into small groups called clusters. One node in the cluster is selected as Cluster Head (CH). The Cluster Head aggregates the data received from other member nodes in the cluster and forwards it to the Sink Node. This helps in conserving the energy of the sensor nodes in the network. If the Cluster Heads are present near to the Sink Node, then they can send the data directly to the Sink Node. Otherwise, the Cluster Heads have to send the data to the Sink Node by using multi-hop communication through other neighboring Cluster Heads. The benefits of Clustering techniques are reduced overhead, decreased delay, efficient utilization of bandwidth leading to reduced energy consumption, increased connectivity, and effective load balancing.
In WSN, however, the number of sensor nodes can be more than hundreds or thousands when used in smart cities, ecological fields, or other revolutionary areas. Therefore, it could be difficult to manage such a large-scale sensor network. In large area WSNs with a high number of nodes, traditional clustering does not provide an efficient solution for managing the network. Also, due to the diversity of WSN applications, finding an appropriate clustering solution remains an open research area.
Grid-based clustering methods are very popular as compared to other conventional methods due to their computational efficiency. In grid-based clustering, a sensing field is partitioned into smaller grids. From each grid, one sensor node is chosen as the Grid Coordinator (Cluster Head), which aggregates the data collected from other sensor nodes that are present in the same grid and routes the aggregated data to the Base Station either single hop or multi-hop. Edla et al 1 listed out the following challenges faced by grid clustering: 1. Determining the best size of grids: If the grid size is too large, more than one cluster could be formed inside one grid cell. On the other hand, if the grid size is small, a single cluster could be spread through more than one grid cell. 2. The locality problem: When the data space has clusters with variable densities and arbitrary shapes, the global density threshold cannot result in clusters with less density. 3. Selecting the merging condition that produces efficient clusters.
Cluster Heads that are closer to the Sink Node face more traffic due to inter-cluster relaying of data from other Cluster Heads to the Sink Node. The Cluster Heads near to the Sink Node drain out energy more quickly than the Cluster Heads that are farther away from Sink Node. This results in more dead nodes near to the Sink Node, which disrupts the network connectivity and causes coverage issues referred to as the Hot Spot problem. Wang et al 2 proposed an Unequal Clustering technique (EDUC) as a solution for the Hot Spot problem. In Unequal Clustering technique, clusters that are closer to the Sink Node are smaller in size, whereas the clusters become larger as the distance between the Sink Node and Cluster Head increases. The cluster size is directly proportional to the distance of Cluster Heads from Sink Node. As Clusters near to the Sink Node are smaller in size, it results in less intra-cluster traffic. Hence these clusters consume less energy for intra-cluster traffic and concentrate more on inter-cluster traffic. Similarly, clusters farther from the Sink Node are larger, and hence they spend more energy on intra-cluster traffic and less energy for inter-cluster traffic. Unequal clustering results in all Cluster Heads in the network to spend a similar amount of energy. Hence, it eliminates Hot Spot problem by balancing the load efficiently among the Cluster Heads. Nazia Majadi et al 3 have proposed a Uniform Cluster Head Distribution technique which helps to conserve the energy needed for intra-cluster transmission of data. If the elected Cluster Heads lie in different areas of the network, then none of the other member nodes in the network have to transmit their data very far to reach their respective Cluster Heads. This will reduce energy consumption as well as increase the node's lifetime.
In recent years, numerous clustering algorithms in WSNs have been proposed, and in most of them, the Cluster Head selection is repeated in each round. Performing selections in each round increases the number of sent and received messages, which will cause problems like increased network traffic, faster depletion of energy in sensor nodes, and an increase in collision.
Clustering Algorithms can be classified as Centralized or Distributed approaches. In distributed clustering algorithms, sensor nodes only use their local information for clustering. Optimal clustering solutions are not possible as the overall view of the WSN is not available. Centralized clustering algorithms depend on the global topology of the network for performing optimal clustering by the Base Station. All the sensor nodes in the WSN should periodically communicate with the Base Station to provide information such as its residual energy, location, and so on. But this additional overhead of communication with the Base Station by the sensor nodes tends to deplete the limited energy of nodes faster, especially in the case of large-area WSN with a high number of nodes.
In this paper, we propose an Energy-Efficient Zone-Based clustering algorithm (EEZBC) for better management of a large area WSN without causing additional burden on the sensor nodes. EEZBC prolongs the network lifetime by efficiently utilizing the energy in sensor nodes. In the proposed method, the sensing field is divided into equal size zones. Each zone is like a smaller size WSN. In each zone, a sensor node with the highest residual energy is selected as the Zone Monitor.
The role of a Zone Monitor is: 1. Determining the number of desired Cluster Heads in its zone The number of desired Cluster Heads in each zone is dependent on the distance of its Zone Monitor from the Base Station and the number of alive sensor nodes in the zone. The distance of each Zone Monitor from the Base Station is considered in the calculation for implementing Unequal Clustering in the given sensing field by giving a higher number of Cluster Heads for zones nearer to the Base Station. The number of desired Cluster Heads in the zones reduces proportionately depending on the increase in distance of respective Zone Monitor from the Base Station. Hence clusters farther away from the Base Station are larger, and they spend more energy on intra-cluster traffic and less energy for inter-cluster traffic.
There are two benefits of having a higher number of Cluster Heads for zones nearer to the Base Station: a. This will result in clusters of smaller size in the zones nearer to the Base Station hence reducing the intra-cluster traffic, which helps in alleviating the Hot Spot problem in the network. b. As a higher number of Cluster Heads are present in zones near to the Base Station, they can share the load of relaying to the Base Station the high traffic arriving at these zones from other faraway zones.

Selecting the Cluster Heads in its zone
In the proposed method, while selecting Cluster Heads, the residual energy of sensor nodes is taken into consideration. Also, the Cluster Heads are selected such that they are uniformly distributed inside each zone to conserve the energy of sensor nodes needed for intra-cluster transmission of data.

Re-Clustering
In the proposed method, re-clustering happens zonewise, and it also reduces the frequency of performing re-clustering. This helps in further minimizing nodes' energy consumption and prolongs network lifetime. In many of the existing methods, a fixed time interval is specified for performing re-clustering, as seen in Reference 4 (Energy-Efficient Grid-Based Routing Algorithm [EEGBR]). But the problem here is that suppose due to more traffic level faced by a Cluster Head if its residual energy drains out before the time interval expires, then the Grid will be without a Cluster Head for that duration. In the proposed method, a minimum threshold value MinTH is determined for the residual energy of Cluster Heads and Zone Monitor. The threshold value MinTH is used for deciding when to trigger re-clustering at zone level. When the Residual Energy of a Cluster Head falls below its threshold value MinTH then it sends a "NoRelay" message to Zone Monitor indicating that it wishes for a role change and in order to conserve its energy the Cluster Head stops serving as a relay device to other Cluster Heads but continues its operation of sensing and operation as a Cluster Head that is data aggregation and forwarding of data received from its cluster. As there are multiple Cluster Heads inside a zone hence even if a Cluster Head stops serving as a relay device, then the traffic reaching the zone from other zones will be relayed by other Custer Heads in the zone. This helps in better coordination and load balancing among the Cluster Heads inside a zone. The Zone Monitor triggers re-clustering in its zone when either of the following conditions is satisfied: a. If it receives "NoRelay" message from 50% or more of Cluster Heads in its zone OR b. If its residual energy falls below its minimum threshold value MinTH, it triggers re-clustering and also selects the next Zone Monitor for its zone The next Zone Monitor will be the sensor node, which is having the highest residual energy in its zone. The minimum threshold value MinTH is further explained in Section 3.4.1.
After the Cluster Heads are selected in a zone, they advertise their selection within their respective zones by sending a message which also contains information about their residual energy and location. For better load balancing among the selected Cluster Heads inside each zone, we propose that cluster size should be uniform at the zone level. Hence, after the advertisement, the remaining Sensor Nodes in a zone decide to become a cluster member of one of the selected Cluster Heads using a distributed fuzzy-based cluster formation technique, which uses Fuzzy inputs: CH Current Energy, Dist. Between Node & CH and CH Load. This is further explained in Section 3.3.
The significant advantages of the proposed algorithm EEZBC are efficient utilization of energy, enhanced packet delivery rate, and an augmentation of the network lifetime.
The remainder of this paper is composed as follows: In Section 2, the literature survey carried out in the areas related to the proposed methodology is briefly explained. In Section 3, the proposed EEZBC is explained. In Section 4, the evaluation of the proposed algorithm and its comparison with other approaches for different network densities is presented. Finally, our conclusions and suggestions for future research are outlined in Section 5.

RELATED WORKS
Heinzelman et al 5 proposed one of the first hierarchical routing mechanisms (LEACH), which is an adaptive clustering algorithm in which, by using probability, a node elects itself to become a Cluster Head and advertises its status in the entire network. During the network lifetime, each node is having a chance of becoming a Cluster Head. The decision to become a Cluster Head depends on the residual energy of the node. Cluster Heads perform the additional task of receiving and aggregating data from all member nodes in the cluster and then transmitting this aggregated data to Sink Node by using Single Hop communication. Cluster Heads consume more energy as compared to other nodes; hence for uniform distribution of load among sensors nodes, LEACH uses a randomized rotation of Cluster Heads. However, both the parameters that are the rotation of Cluster Heads and residual energy of nodes are not sufficient for even distribution of load in the network. The major drawback of LEACH is that it may elect a higher number of Cluster Heads than the desired number resulting in higher energy consumption. Also, the uniform distribution of CHs is needed throughout the network; otherwise, some sensor nodes lying far away from all the selected CHs consume more energy for transmission of data. Other drawbacks of LEACH are lower stability region and high transmission power required in the case of a large sensing field. Younis and Fahmy 6 (HEED) proposed a distributed clustering approach that considers two parameters residual energy and intra-cluster communication cost for clustering. The main drawback of HEED is that a member node transmits the data to multiple Cluster Heads if it is within their transmission range. This results in the redundancy of communicated data.
Soro and Heinzelman 7 proposed an energy-efficient protocol (UCS) which is applicable for both homogenous and heterogeneous networks. In heterogeneous networks, it requires nodes with more energy called as super nodes to be positioned at some predetermined locations. However, it is difficult to meet this requirement in real life for WSNs as sensor nodes are usually deployed uniformly and randomly over the sensing field.
Wang et al 2 proposed an Unequal clustering protocol (EDUC). IN EDUC, each node can become a CH only once. The Cluster Heads have an unequal competition radius in which clusters are formed. As EDUC uses single-hop communication, it consumes more energy for transmitting data to the Sink Node especially when the sensing field is large.
Khan et al 8 proposed an Energy-Efficient routing protocol AZR-LEACH. In this approach, a large sensing field is divided into rectangular clusters. Further, these rectangular clusters are grouped into zones. This helps in selecting an optimal number of CHs in the sensing field and efficient communication between CHs and Sink Node.
Mhemed et al 9 proposed an energy-efficient cluster formation protocol that uses Fuzzy logic (FLCFP). The fuzzy inference system in FLCFP for cluster formation considers three parameters Energy level, Distance to Base station, and Distance to CH. The drawback of FLCFP is that it does not take into consideration the cluster size during cluster formation. However, it is an important parameter that must be considered for the efficient energy utilization of the sensor nodes in WSN.
Yuan-Po Chi et al 10 proposed a Grid-based Routing Scheme for WSN that tries to conserve energy in the context of dynamic topology. Ortiz et al 11 proposed a routing algorithm that performs role assignments during route establishment and maintenance. This approach makes use of fuzzy logic for role assignment. Efficient routing approaches are used for extending the lifetime of the network by efficient utilization of energy and uniform balancing of the load. Fuzzy logic provides a simple technique that is similar to human logic for making a decision from vague input data. Nazia Majadi et al 3 have proposed a uniform distribution technique of CHs during selection to reduce energy consumption as well as increase the node's lifetime. However, in this technique, the clusters formed may not be uniform. Usually, protocols that use clustering techniques have variable-sized clusters, for example, in LEACH 5 and HEED 6 ; hence they need variable-sized packets for the transmission of aggregated data. However, the packet sizes in WSNs must be small and of fixed length due to resource constraints. In the proposed approach, inside each zone, there is a uniform distribution of CHs and uniform sized clusters.
Izadi et al 12 proposed a new cluster formation method in which on receiving the willing to join message, the Cluster Head permits the sensor node to join its cluster. But they have not specified on what basis the node can join the Cluster Head.
Ahmed et al 13 proposed a Distributed clustering algorithm (SEED) in which sensor nodes with the same application form sub-clusters. The sensor nodes will be sleeping to save their resources. In each round, one sensor node from these sub-cluster awakes and transmits the data. This helps in reducing the number of transmissions toward the Sink Node. In SEED, the sensing field is divided into three energy regions, and CHs use single-hop communication with the Sink Node. The Cluster Heads of the high energy region is communicating with the Sink Node through a longer distance as compared to the Cluster Heads of the low energy region. Researchers have used Grid-based routing techniques for optimizing routing performance.
Hamzah et al 14 have proposed fuzzy logic-based energy-efficient clustering for WSNs. They have proposed a clustering technique that uses Fuzzy Logic for the election of Cluster Head and enforces a separation distance between them for even Cluster Head distribution in the sensing region. For the Fuzzy Controller, the five linguistic variables they use are residual energy, distance from the Base Station, location suitability, the density of surrounding nodes, and compaction of surrounding nodes.
Aierken et al 15 proposed a rotated unequal clustering protocol in order to reduce the energy hole problem called RUHEED. It composed of three phases that are Cluster Head election, cluster formation, and rotation. The advantage of RUHEED is that it reduces the number of control messages by reducing the number of Cluster Head election and cluster formation phases.
El Alami et al 16 proposed a Fuzzy Logic-based Clustering Algorithm called CAFL for improving network lifetime. This approach uses fuzzy logic for Cluster Head selection and cluster formation process. For Cluster Head selection, the fuzzy controller uses residual energy and closeness to the sink as fuzzy inputs. For cluster formation, it uses residual energy of Cluster Head and proximity to Cluster Head as fuzzy inputs.
Balakrishnan et al 17 proposed a Fuzzy Logic-Based Energy Efficient Clustering Hierarchy algorithm called FLECH for non-uniform Wireless Sensor Network. FLECH uses residual energy, node centrality, and distance to Base Station as fuzzy input parameters for electing suitable nodes as Cluster Head for improving the network lifetime.
Zhang et al 18 proposed an energy efficient distributed clustering algorithm based on a fuzzy approach with a non-uniform distribution called EEDCF. It defines four different states for each node: the initial state, the competing Cluster Head state, the elected Cluster Head state, and the member node state. Also, in this approach, the cluster formation process is divided into three phases: updating the information table, Cluster Head election, and cluster building. During Cluster Heads' election, this method considers nodes' energies, nodes' degree, and neighbor nodes' residual energies as the fuzzy input parameters.
Logambigai et al 4 proposed a Grid-based routing algorithm that applies fuzzy rules and unequal clustering of nodes for increasing the network lifetime. In this approach, the Grid coordinator applies Fuzzy rules to find the optimal path to the Sink Node by reducing the number of hops.

MATERIALS AND METHODS
In this section, the proposed EEZBC is explained. The main objective is the efficient utilization of energy in sensor nodes to prolong the network lifetime. The workflow of the proposed algorithm is illustrated in Figure 1. and pseudocode is presented after that. Sensor Nodes are uniformly and randomly deployed in the sensing field. The sensing field is divided into equal size zones.
The proposed algorithm works in four phases: First phase: One Zone Monitor is selected in each Zone (Pseudocode 1).

F I G U R E 1 Workflow of the proposed algorithm EEZBC
Third Phase: Clusters are formed that is the remaining Sensor Nodes in Zone become a member of one of the selected Cluster Heads in the Zone (Pseudocode 3).
Fourth Phase: Re-Clustering is done when Residual Energy of Cluster Heads or Zone Monitor fall below their minimum threshold value (Pseudocode 4).
The following assumptions are made in the proposed work: 1. The sensor nodes should be deployed randomly and uniformly in an x × x plane field. 2. The Base Station and all the sensor nodes are stationary. 3. Sensor nodes send data packets to Base Station, which is located outside the sensor field. 4. All sensor nodes have a communication range and have stable bidirectional links with the neighboring nodes. 5. All the sensors nodes and Base Station are location-aware. 6. The dimensions of the sensor field should be provided initially. 7. The coordinates of the Base Station should be known. 8. Sensor Nodes can vary the amount of transmission power by using power control.
The energy model used in the proposed work is adopted from LEACH. 5 For transmission of an l bit message to a distance of d the radio dissipates energy as follows, 5 where E elec is the energy dissipation to run the radio electronics, and fs and mp are the energy dissipation values to run the amplifier for close and far distances, respectively. Depending on the distance between the transmitter and receiver, free space ( fs ) or multi-path fading ( mp ) channel models are used. 5 For receiving an l bit message, the radio dissipates energy as follows 5 : Figure 1 illustrates the overall workflow of the proposed algorithm EEZBC.
The basic architecture of a sample Wireless Sensor Network used in proposed work is shown in Figure 2. As shown in Figure 2., the sensing field is 400 × 400 m 2 in which 215 Sensor Nodes are uniformly and randomly deployed. The Base Station is located at 200 m × 400 m.
The proposed algorithm EEZBC works well for a large sensing field as well. The sensing field is divided into equal size zones, as shown in Figure 3. These zones are heterogeneous that is each zone may have a different number of sensor nodes. The zone size can be preferably either 100 × 100 m 2 or 50 × 50 m 2 . The given sensing field area can be rounded off to the nearest multiple of 50.
As shown in Figure 3., the sensing field of 400 × 400 m 2 is divided into equal size zones of 100 × 100 m 2 resulting in 16 zones that are labeled as Z1 to Z16.

Zone monitor selection
During the initialization phase, one sensor node in each zone having the highest Residual Energy is selected as Zone Monitor (ZM), as shown in Figure 4. The following Pseudocode 1 gives details about this selection in the First Phase. After the selection, each ZM(i) calculates its threshold value MinTH_ZM(i) using Equation (3) given below. When the Residual Energy of a Zone Monitor falls below its threshold value, then it triggers the re-clustering phase in its zone.
END FOR

Cluster head selection
The number of Cluster Heads (CH), num_CH_Z(i) to be selected in Zone Z(i) is dependent on the distance of its Zone Monitor, ZM(i) from the Base Station and the number of alive sensor nodes in the zone and is given by Equation (4). The reserved circular area of radius r(i) for each Cluster Head to be selected in Zone Z(i) is given by Equation (5).
Next, Cluster Heads are selected in each zone, as shown in Figure 5. Leaving out the Sensor Node selected as Zone Monitor, from the remaining Sensor Nodes in Zone Z(i), the node having the highest Residual Energy is chosen as the first Cluster Head. The newly selected Cluster Head in Zone Z(i) reserves around itself a circular area of radius r(i). From the remaining sensor nodes, find the node which is not in the reserved area of already selected Cluster Heads and having the highest Residual Energy and select it as new Cluster Head. Continue the selection process till num_CH_Z(i) Cluster Heads are selected for zone Z(i). After the selection, each Cluster Head CH(i)(j) calculates its threshold value MinTH_CH(i)(j) using Equation (6) given below.
The following Pseudocode 2 gives details about the Second phase. During the Initialization phase, Pseudocode 2 is executed for all the zones in the sensing field.

Pseudocode 2 num_CH_Z(i) is Number of Cluster Heads to be selected in zone Z(i) num_SN_Z(i) is Number of alive Sensor Nodes in zone Z(i) L is the side of sensing field distBStoZM(i) is the distance between Base Station and ZM(i) r(i) is the radius of reserved circular area of each Cluster Head in zone Z(i) Length Z is Length of zone Z CH(i)(j) is jth Cluster Head of zone Z(i) MinTH_CH(i)(j) is threshold value MinTH for CH(i)(j) ResidualEnergy_CH(i)(j) is residual energy of CH
FOR each integer j in num_CH_Z(i) DO CH(i)(j) ← Sensor Node which is not in the reserved area r(i) of already selected Cluster Heads in zone Z(i) and having highest residual energy among the remaining nodes (leaving out ZM(i)) END FOR

Unequal clustering in the sensing field
We propose Equation (4) for implementing Unequal Clustering in the given sensing field. Equation (4) gives a higher number of Cluster Heads for zones near to the Base Station. A higher number of Cluster Heads in a zone will result in a higher number of clusters of smaller sizes in the zone. Hence, the zones near to the Base Station have smaller sized clusters, whereas Zones away from the Base Station have bigger sized clusters. As clusters near to the Base Station are smaller in size, it results in less intra-cluster traffic. Hence these clusters consume less energy for intra-cluster traffic and concentrate more on inter-cluster traffic. Similarly, clusters farther away from the Base Station are larger in size, and hence they spend more energy on intra-cluster traffic and less energy for inter-cluster traffic. Also, as a higher number of Cluster Heads are present in zones near to the Base Station, they can share the load of relaying the high traffic arriving at these zones from other faraway zones. This helps in alleviating the Hot Spot problem usually faced by sensor nodes that are near to the Base Station. In Equation (4), we use the parameter "0.4 * num_SN_Z(i)" for selecting 40% of the alive sensor nodes as Cluster Heads in Zones that are closest to the Base Station. As the distance of zone increases from the Base Station, the number of Cluster Heads selected in the zone decreases. After repeating the experiment for different values, it was concluded that choosing the starting value as 40% for selecting the number of Cluster Heads in the zones that are closest to Base Station gave the best result. Example: Figure 5 shows a sensing field of 400 × 400 m 2, which is divided into equal size zones of 100 × 100 m 2 . For Zone Z(10) the number of Cluster Heads num_CH_Z(10) is determined by using Equation (4)  Hence zone Z(10) will have three Cluster Heads and one Zone Monitor, as shown in Figure 5.

Uniform cluster head distribution
Nazia Majadi et al 7 have proposed a uniform distribution technique of Cluster Heads at the time of selection. In this approach, the sensor node, which has the maximum residual energy, is selected as the first Cluster Head and advertises its selection. Then the first Cluster Head selects an area, no other node in that particular area can advertise itself as CH. Another Cluster Head is selected after this from the remaining network. The whole WSN is divided in this way into some predefined areas. Each predefined area contains only one Cluster Head, and all the sensor nodes in that area form a cluster. 7 In the proposed algorithm EEZBC, this technique is incorporated with some modifications. Let us call this selected area as the "reserved area" of a Cluster Head. In the proposed approach, the size of the reserved circular area for all the Cluster Heads belonging to a zone is the same and is dependent on the number of Cluster Heads in that zone. The radius r of reserved circular area for all the Cluster Heads in a zone is given by Equation (2).
Example: As seen in Figure 5, Zone Z(10) has three Cluster Heads. The reserved circular area of radius r(10) for each Cluster Head selected in Zone Z(10) is given by Equation (5).

Uniform sized cluster formation at zone level
The selected Cluster Heads then advertise their selection within their respective zones by sending a message which also contains information about their residual energy and location. After the advertisement, the remaining Sensor Nodes in a zone decide to become a cluster member of one of the selected Cluster Heads using a distributed fuzzy-based cluster formation technique, which uses Fuzzy inputs: CH Current Energy, Dist. Between Node & CH and CH Load. The CH Load of a Cluster Head is given by Equation (7). The following Pseudocode 3 provides details about the Third phase.

becomes a member of Cluster for Cluster Head 'Selected_CH' END IF END FOR
Usually, Cluster-based protocols have highly variable-sized clusters. This results in an unequal distribution of load among the Cluster Heads. Hence the proposed algorithm after selection of Cluster Heads uses a fuzzy-based cluster formation technique for the formation of uniformly sized clusters at the zone level. It uses Fuzzy inputs: CH Current Energy, Dist. Between Node & CH and CH Load. The proposed algorithm EEZBC optimizes energy utilization in sensor nodes by keeping the cluster size uniform at the zone level. The sensor nodes before joining a cluster, consider the count of the members that are already present in the respective cluster. Thangaramya et al 19 have proposed calculation of CH Degree for uniform cluster formation in the whole sensing area field. In the proposed method EEZBC, CH Load is calculated at zone level and is given by Equation (7). In Equation (7) CH Load is calculated by considering the number of member nodes already belonging to a cluster relative to the total number of nodes present in the respective zone. By considering CH Load as one of the fuzzy inputs in Fuzzy-Based Cluster Formation technique, it ensures that uniform clusters are formed at the Zone level. After clusters are formed, the member Sensor Nodes based on the local TDMA schedule transmit their data to their respective Cluster Head, which aggregates the data and transmits it in multiple hops through neighboring Cluster Heads to the Base Station. Any existing multi-hop hierarchical routing algorithm can be used along with the proposed clustering algorithm for relaying data from source to Base Station.

Re-clustering
For Zone Z(i), when the Residual Energy of a Cluster Head CH(i)(j) falls below its threshold value MinTH_CH(i)(j), it does two things: a. It sends a message "NoRelay" to its Zone Monitor ZM(i), informing that its Residual Energy is less than its threshold value, and it wishes for a role change. b. The Cluster Head CH(i)(j), to conserve its energy, stops serving as a relay device to other Cluster Heads but continues its operation of sensing and operation as a Cluster Head that is data aggregation and forwarding of data received from its cluster.
As there are multiple Cluster Heads inside a zone hence even if a Cluster Head stops serving as a relay device, then the traffic reaching the zone from other zones will be relayed by other Custer Heads in the zone. This helps in better coordination and load balancing among the Cluster Heads inside a zone.
Zone Monitor ZM(i) triggers re-clustering in its zone Z(i) under the conditions as given below in Pseudocode 4. The re-clustering phase for Zone Z(i) is given by Pseudocode 2. In the proposed method EEZBC, re-clustering happens zonewise and it also reduces the frequency of performing re-clustering. This helps in further minimizing nodes' energy consumption and prolongs network lifetime. The following Pseudocode 4 gives details about the fourth phase. 1. If it receives 'NoRelay' message from 50% or more of Cluster Heads in its zone Z(i) OR 2. If its residual energy falls below its minimum threshold value MinTH_ZM(i), it triggers re-clustering and also selects the next Zone Monitor for its zone Z(i). The next Zone Monitor will be the sensor node having the highest residual energy in its zone Z(i).

Threshold value MinTH for re-clustering
The minimum threshold value MinTH is determined for the residual energy of Cluster Heads and Zone Monitor. It is not practical to have a single minimum threshold value, MinTH for all the zones in the whole network as the traffic level faced by the nodes is variable in different regions of the sensing field. Hence a single MinTH value for the complete network is not a good option. Let us consider the option of having a single threshold value MinTH at the zone level. For example, suppose we select at the zone level a low threshold value MinTH of 0.2 J. In this case, during the start-up phase, when the nodes which are selected as Zone Monitor and Cluster Heads are having initial energy of 1 J, they will continue in the same role till their residual energy falls below MinTH value of 0.2 J. This results in improper sharing of load by the nodes in the zone. Hence, having a low threshold value MinTH at zone level is not a good option.
Consider another example, suppose we select at zone level a higher threshold value MinTH of 0.4 J. But this will cause a problem when all the nodes in the zone are having residual energy less than or equal to MinTH value of 0.4 J. None of them will serve as a relay device to conserve their remaining energy. Hence, having a high threshold value MinTH at zone level is also not a good option.
Therefore, in the proposed algorithm EEZBC, MinTH value is calculated individually for each selected Zone Monitor and Cluster Heads and is given by Equation (3) for Zone Monitor and Equation (6) for Cluster Heads. In each zone, sensor nodes having comparatively higher Residual Energy are selected as Zone Monitor and Cluster Heads. The threshold value MinTH is set to half of the residual energy of the respective node. There are multiple Cluster Heads in each zone, and re-clustering will be done zonewise, when residual energy of 50% or more of Cluster Heads in a zone falls below its MinTH value or if residual energy of Zone Monitor itself falls below its MinTH value. This reduces the frequency of re-clustering and ensures efficient load balancing among the sensor nodes in the network and prolong sensors lifetime when it is worthy to keep them alive.

Fuzzy inference system for cluster formation
After num_CH_Z(i) number of Cluster Heads are selected in zone Z(i), the Cluster Heads advertise their selection within their respective zones by sending a message which also contains information about their residual energy and location. The remaining sensor nodes in zone Z(i) decide to become cluster member of one of the selected Cluster Heads by using a distributed Fuzzy Inference system which uses Fuzzy inputs: CH Residual Energy, distance between Node & CH and CH Load. Sensor nodes before joining a cluster check the count of the members which are already present in the cluster. This is called as CH Load and is calculated by using Equation (7). The minimum and maximum values of input parameters given to the fuzzy inference system for determining Cluster Head are shown in Table 1. Using Min-Max normalization, the values of input parameters are normalized to decimal values between 0 and 1. The input range for each of the fuzzy input variables is given in Table 2. The fuzzy input variables and its linguistic variables used for determining Cluster Head are as follows: Distance to CH-(close, medium, far) CH Residual Energy-(low, medium, high) CH load-(low, medium, high) For the fuzzy variables, the triangular function is used for intermediate variables, and trapezoidal member function is used for the boundary variables.
The linguistic variable Distance_CH and its values used are depicted in Figure 6. The values used for this fuzzy set are Close, Medium, and Far.
The linguistic variable CH Residual Energy and its values used are depicted in Figure 7. The values used for this fuzzy set are Low, Medium, and High.
The linguistic variable CH Load and its values used are depicted in Figure 8. The values used for this fuzzy set are Low, Medium, and High.
The output variable CH_Choice and its values used are depicted in Figure 9. The values used for this fuzzy set are Most Likely, More Likely, Likely, Medium Likely, Medium Less Likely, Medium Lesser Likely, Less Likely, Lesser Likely, Least Likely.
The fuzzy rules for output variable CH_Choice are given in Table 3. Mamdani inference system is used for the fuzzy logic and the defuzzification method used here is the Center of Area method. This method finds the center of area of a fuzzy set and returns the corresponding crisp value.

RESULTS AND DISCUSSION
The proposed method EEZBC has been simulated using Matlab. The Network Simulation parameters are given in Table 4. Simulation is carried out for different network densities from 150 to 350 sensor nodes that are randomly deployed over a region of 400 × 400 m 2 . The simulation result is the average of 100 independent experiments. The proposed technique is evaluated, and the trial results are exhibited. We considered the metrics of lifetime and total consumed energy to evaluate the proposed method EEZBC comparatively with existing schemes. Figure 10 shows a Simulation area of 400 × 400 m 2 that is divided into equal size zones of 100 × 100 m 2 . The Zone Monitor selected for each zone is set to green color. Cluster Heads selected in each zone is set to cyan color. Sensor nodes that are currently generating packets are seen in yellow color. The CHs that are selected for routing are set to red color. The Base Station or Sink Node is located outside the sensing field at the edge given by coordinates (400 × 400) m.
The proposed algorithm EEZBC is compared with the algorithms EEGBR, 4 MCFL, 20 and LEACH. 13 The experiment is carried out for more than 2000 rounds. Experimental results demonstrate that EEZBC performs better than other existing algorithms which are used for comparison purposes. The proposed algorithm is comparatively evaluated under different network densities to illustrate and validate its behavior. The comparison based on the network lifetime metric is in terms of FND, HND, and LND for network density of 150, 250, and 350 nodes. Figures 11-13  lifetime of the proposed method EEZBC for FND, HND, and LND, respectively, against the achieved average lifetime of LEACH, MCFL, and EEGBR for the different network densities. It is clear from these three figures that the proposed method achieved a longer average of network lifetime for each of the terms FND, HND, and LND for all network densities. Consider Figure 11, we see that the network lifetime achieved by the proposed method in terms of FND for the network having 150 nodes is better than EEGBR about 33%, MCFL about 100%, and LEACH about 433%. The network lifetime achieved by the proposed method in terms of FND for the network having 250 nodes is better than EEGBR about 42%, MCFL about 105%, and LEACH about 429%. Similarly, for FND, network lifetime achieved for 350 nodes by the proposed method is better than EEGBR about 45%, MCFL about 110%, and LEACH about 500%.
Consider Figure 12, we see that the network lifetime achieved by the proposed method in terms of HND for the network having 150 nodes is better than EEGBR about 74%, MCFL about 160%, and LEACH about 748%. The network lifetime achieved by the proposed method in terms of HND for the network having 250 nodes is better than EEGBR about 79%, MCFL about 178%, and LEACH about 764%. Similarly, for HND, network lifetime achieved for 350 nodes by the proposed method is better than EEGBR about 81%, MCFL about 179%, and LEACH about 765%.
Consider Figure 13, we see that the network lifetime achieved by the proposed method in terms of LND for the network having 150 nodes is better than EEGBR about 6%, MCFL about 25%, and LEACH about 76%. The network lifetime achieved by the proposed method in terms of LND for the network having 250 nodes is better than EEGBR about 18%, MCFL about 33%, and LEACH about 77%. Similarly, for LND, network lifetime achieved for 350 nodes by the proposed method is better than EEGBR about 19%, MCFL about 34%, and LEACH about 79%. Figure 14 demonstrates the overall achieved enhancement of the proposed method EEZBC against LEACH, MCFL, and EEGBR for the network lifetime metric in terms of FND, HND, and LND for the different network densities. It is evident from the Figures 11-14 that EEZBC has outperformed the other existing schemes. The improvements achieved by EEZBC is due to its ability of load balancing and efficient utilization of energy in the sensor nodes.  Figure 15 shows the number of alive nodes against the number of rounds for the various methods for a network density of 250 nodes. After 1200 rounds, EEGBR algorithm has 53 nodes alive, in M2CM 28 nodes and in LEACH 10 nodes are alive. But in the proposed method 135 nodes are alive which is higher than the other algorithms. At 1200 rounds, based on Alive Nodes metric, proposed method is improved over EEGBR by about 155%, over M2CM by about 382%, and over LEACH by about 1250%. Figure 16 shows the amount of data packets received by the Base Station for a network density of 250 nodes. From the figure it is clearly observed that the proposed method EEZBC improves the amount of data packets received at Base Station compared with EEGBR, MCFL, and LEACH. At 1000 rounds, the amount of Packet Delivery Rate (PDR) in the proposed method is improved by 27%, 76%, and 225% compared with EEGBR, MCFL, and LEACH respectively. Figure 17 depicts the percentage of total remaining energy per round. The figure shows that the proposed method conserves more energy than the other three schemes.
The reason for performance improvement in EEZBC is that it implements Unequal Clustering in Sensing Field, Uniform Cluster Head Distribution in zone, and Uniform Clustering at zone level. Every time re-clustering is done new Cluster Heads have to be selected. In the proposed method, we have kept Cluster Head selection simple. In EEZBC, the Zone monitor takes care of Cluster Head selection in its zone. While selecting the Cluster Heads the residual energy of sensor nodes is taken into consideration. Also, the Cluster Heads are selected such that they are uniformly distributed inside each zone to conserve the energy of sensor nodes needed for intra-cluster transmission of data. As we have assumed random and uniform deployment of sensor nodes in the sensing field; hence when uniformly distributed Cluster Heads are selected in each zone this results in proper coverage of every region in the zone. Uniform distribution of Cluster Heads in the sensing field will also help when data are relayed to Base Station using multi-hop routing, especially in the F I G U R E 16 Amount of data received at base station F I G U R E 17 Percentage of total remaining energy per round case of large area WSN. In the proposed method, the cluster size is kept uniform at zone level for better load balancing among the selected Cluster Heads inside each zone. Also, re-clustering happens zonewise and the frequency of performing re-clustering is reduced. This helps in further minimizing nodes' energy consumption and prolongs network lifetime.

CONCLUSION AND FUTURE WORK
In WSN, the number of sensor nodes can be more than hundreds or thousands when used in fields like smart cities, ecological fields, and so on. Traditional clustering does not provide an efficient solution for managing the network in large area WSNs with high number of nodes. In the proposed EEZBC, the sensing field is divided into equal size zones. In each zone, a sensor node with the highest residual energy is selected as the Zone Monitor. The number of desired Cluster Heads in each zone is dependent on the distance of its Zone Monitor from the Base Station and the number of alive sensor nodes in the zone. The distance of each Zone Monitor from the Base Station is considered in the calculation for implementing Unequal clustering in the given sensing field by giving a higher number of Cluster Heads for zones nearer to the Base Station. This will result in clusters of smaller size in the zones nearer to the Base Station. Hence these clusters consume less Energy for intra-cluster traffic and concentrate more on inter-cluster traffic. Also, as a higher number of Cluster Heads are present in zones near to the Base Station, they can share the load of relaying the high traffic arriving at these zones from other far away zones. This helps in alleviating the Hot Spot problem usually faced by sensor nodes that are near to the Base Station. The Cluster Heads are selected such that they are uniformly distributed inside each zone to conserve the energy of sensor nodes needed for intra-cluster transmission of data. In the proposed method re-clustering happens zonewise and it also reduces the frequency of performing re-clustering. This helps in further minimizing nodes' energy consumption and prolongs network lifetime. The advantages of the proposed algorithm are efficient utilization of energy, enhanced packet delivery rate, and an augmentation of the network lifetime. The proposed algorithm has been assessed through simulations carried out using Matlab and it is found to be more efficient as compared to other related works in terms of energy utilization, increased network lifetime, and packet delivery rate. In the proposed work, we are using Fuzzy Inference system for Cluster formation. In future work, we can extend this algorithm by using FIS for Cluster Head Selection also. The proposed method can also be extended for sensor networks with mobile nodes.

PEER REVIEW INFORMATION
Engineering Reports thanks the anonymous reviewers for their contribution to the peer review of this work.

CONFLICT OF INTEREST
The author declares no potential conflict of interest.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.